JEE MAIN Statistics Measures Of Central Tendency Previous Year Questions (PYQs) – Page 1 of 8
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The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :
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Solution
Let the mean and the standard deviation of the observation $2,3,3,3,4,5,7,a,b$ be $4$ and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is:
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Solution
If $\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$ and $\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$(n, a > 1) then the standard deviation of n observations x1, x2, ..., xn is :
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Solution
If mean and standard deviation of 5 observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$ respectively, then the variance of 6 observations $x_1,x_2,\ldots,x_5$ and $-50$ is equal to :
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Solution
All the students of a class performed poorly in Mathematics. The teacher
decided to give grace marks of $10$ to each of the students. Which of the
following statistical measures will not change even after the grace marks were
given?
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Solution
The outcome of each of 30 items was observed; 10 items gave an outcome $\dfrac{1}{2}-d$ each, 10 items gave outcome $\dfrac{1}{2}$ each and the remaining 10 items gave outcome $\dfrac{1}{2}+d$ each. If the variance of this outcome data is $\dfrac{4}{3}$ then $|d|$ equals :
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Solution
The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively.
The mean and variance of another set of $15$ numbers are $14$ and $\sigma^{2}$ respectively.
If the variance of all the $30$ numbers in the two sets is $13$, then $\sigma^{2}$ is equal to:
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Solution
The mean and standard deviation of $100$ observations are $40$ and $5.1$, respectively. By mistake one observation is taken as $50$ instead of $40$. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $10(\mu+\sigma)$ is equal to
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Solution
The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. Then $\lambda$ is equal to :
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Solution
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if $\alpha$ and $\sqrt \beta $ are the mean and standard deviation respectively for correct data, then ($\alpha$, $\beta$) is :
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Solution
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